Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. The Howard methods also assume that the species composition of the harvests are equal to the species composition of released fish, which may not be true and is evident in the logbook data. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds that when not met, values are borrowed from nearby areas Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is no uncertainty generated from uncertainty in the assmptions made such as species composition of the releases or when borrowing values from one area to another. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.
Time series 1999 - present 1977 - present

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was explored that loosened the assumption that logbook releases were a census. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Priors.

Priors range from uninformative to very informative or fixed. These will be covered once a satisfactorilly convergerd model is achieved.

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behavior and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 8.**- DSR rockfish (including yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 10.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 12.**- Residuals from logbook harvests

Figure 12.- Residuals from logbook harvests


SWHS residuals

**Figure 13.**- Residuals from SWHS harvests.

Figure 13.- Residuals from SWHS harvests.



**Figure 14.**- Residual of SWHS releases

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 15.**- Mean percent of harvest by charter anglers.

Figure 15.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 16.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 18.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 19.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 20.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


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SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 23.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 24.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 25.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 26.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 27.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 28.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 30.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 31.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_yellow 1 1.657283
beta2_yellow 1 1.650477
beta1_yellow 2 1.621073
beta2_black 2 1.302493
tau_beta0_pH 1 1.178144
beta1_pH 3 1.176551
parameter n badRhat_avg
beta3_yellow 1 1.161338
beta1_pelagic 1 1.140638
beta2_pelagic 2 1.137026
beta0_pelagic 1 1.135795
beta2_pH 1 1.120275
Table 2. Summary of unconverged parameters by area
BSAI CI NSEI NSEO PWSI PWSO WKMA
beta0_pelagic 0 0 0 0 1 0 0
beta0_yellow 0 0 0 0 0 1 0
beta1_pelagic 0 0 0 0 1 0 0
beta1_pH 1 0 0 0 1 1 0
beta1_yellow 0 1 0 0 0 1 0
beta2_black 0 1 1 0 0 0 0
beta2_pelagic 0 0 0 1 0 1 0
beta2_pH 0 0 0 0 0 0 1
beta2_yellow 0 0 0 1 0 0 0
beta3_yellow 0 0 0 0 0 1 0
tau_beta0_pH 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.122 0.074 -0.259 -0.125 0.033
mu_bc_H[2] -0.096 0.045 -0.175 -0.099 0.002
mu_bc_H[3] -0.434 0.071 -0.569 -0.436 -0.292
mu_bc_H[4] -0.979 0.192 -1.364 -0.973 -0.613
mu_bc_H[5] 0.939 0.930 -0.153 0.749 3.035
mu_bc_H[6] -2.157 0.321 -2.791 -2.161 -1.502
mu_bc_H[7] -0.443 0.110 -0.666 -0.441 -0.235
mu_bc_H[8] 0.248 0.396 -0.356 0.212 1.116
mu_bc_H[9] -0.292 0.137 -0.560 -0.289 -0.019
mu_bc_H[10] -0.106 0.069 -0.233 -0.108 0.036
mu_bc_H[11] -0.124 0.038 -0.198 -0.123 -0.049
mu_bc_H[12] -0.253 0.108 -0.485 -0.247 -0.052
mu_bc_H[13] -0.135 0.077 -0.283 -0.136 0.020
mu_bc_H[14] -0.307 0.098 -0.507 -0.306 -0.117
mu_bc_H[15] -0.342 0.049 -0.433 -0.342 -0.247
mu_bc_H[16] -0.263 0.385 -0.887 -0.300 0.561
mu_bc_R[1] 1.353 0.149 1.074 1.352 1.645
mu_bc_R[2] 1.454 0.092 1.266 1.456 1.631
mu_bc_R[3] 1.394 0.145 1.101 1.395 1.686
mu_bc_R[4] 0.902 0.201 0.482 0.911 1.281
mu_bc_R[5] 1.179 0.470 0.267 1.190 2.109
mu_bc_R[6] -1.589 0.428 -2.434 -1.585 -0.767
mu_bc_R[7] 0.394 0.187 0.012 0.401 0.738
mu_bc_R[8] 0.559 0.193 0.166 0.567 0.907
mu_bc_R[9] 0.345 0.204 -0.080 0.356 0.716
mu_bc_R[10] 1.292 0.140 1.014 1.295 1.560
mu_bc_R[11] 1.039 0.095 0.854 1.038 1.227
mu_bc_R[12] 0.817 0.202 0.402 0.822 1.197
mu_bc_R[13] 1.029 0.102 0.826 1.031 1.230
mu_bc_R[14] 0.895 0.140 0.611 0.897 1.165
mu_bc_R[15] 0.784 0.110 0.562 0.784 1.007
mu_bc_R[16] 1.089 0.126 0.844 1.089 1.339
tau_pH[1] 5.208 0.447 4.377 5.191 6.112
tau_pH[2] 2.055 0.221 1.645 2.042 2.522
tau_pH[3] 2.249 0.221 1.841 2.242 2.707
beta0_pH[1,1] 0.564 0.177 0.212 0.567 0.899
beta0_pH[2,1] 1.367 0.184 0.986 1.371 1.714
beta0_pH[3,1] 1.426 0.202 0.977 1.442 1.767
beta0_pH[4,1] 1.573 0.208 1.112 1.585 1.946
beta0_pH[5,1] -0.867 0.286 -1.497 -0.845 -0.361
beta0_pH[6,1] -0.655 0.419 -1.660 -0.597 -0.029
beta0_pH[7,1] -0.511 0.496 -1.603 -0.484 0.461
beta0_pH[8,1] -0.668 0.299 -1.333 -0.638 -0.201
beta0_pH[9,1] -0.655 0.278 -1.255 -0.636 -0.167
beta0_pH[10,1] 0.224 0.205 -0.194 0.226 0.604
beta0_pH[11,1] -0.094 0.169 -0.434 -0.092 0.228
beta0_pH[12,1] 0.487 0.184 0.129 0.496 0.842
beta0_pH[13,1] -0.004 0.148 -0.299 -0.002 0.276
beta0_pH[14,1] -0.313 0.162 -0.642 -0.308 0.002
beta0_pH[15,1] -0.039 0.177 -0.399 -0.037 0.299
beta0_pH[16,1] -0.504 0.385 -1.424 -0.422 0.049
beta0_pH[1,2] 2.805 0.167 2.465 2.812 3.121
beta0_pH[2,2] 2.879 0.134 2.618 2.879 3.141
beta0_pH[3,2] 3.118 0.179 2.776 3.122 3.438
beta0_pH[4,2] 2.940 0.130 2.676 2.939 3.185
beta0_pH[5,2] 4.751 1.414 3.044 4.405 8.373
beta0_pH[6,2] 3.115 0.202 2.735 3.113 3.518
beta0_pH[7,2] 1.956 0.170 1.618 1.958 2.296
beta0_pH[8,2] 2.872 0.175 2.527 2.874 3.227
beta0_pH[9,2] 3.430 0.222 3.001 3.426 3.874
beta0_pH[10,2] 3.743 0.194 3.379 3.741 4.126
beta0_pH[11,2] -4.866 0.302 -5.470 -4.854 -4.278
beta0_pH[12,2] -4.791 0.387 -5.575 -4.784 -4.066
beta0_pH[13,2] -4.571 0.396 -5.347 -4.573 -3.798
beta0_pH[14,2] -5.625 0.463 -6.605 -5.605 -4.792
beta0_pH[15,2] -4.280 0.343 -4.938 -4.282 -3.616
beta0_pH[16,2] -4.880 0.397 -5.683 -4.870 -4.132
beta0_pH[1,3] 0.226 0.839 -1.778 0.339 1.360
beta0_pH[2,3] 2.197 0.155 1.897 2.197 2.501
beta0_pH[3,3] 2.524 0.144 2.248 2.525 2.802
beta0_pH[4,3] 2.967 0.160 2.655 2.966 3.293
beta0_pH[5,3] 1.423 1.713 -1.077 1.143 5.675
beta0_pH[6,3] -0.827 0.861 -2.175 -0.953 1.370
beta0_pH[7,3] -1.815 0.426 -2.686 -1.802 -0.997
beta0_pH[8,3] 0.282 0.186 -0.094 0.281 0.652
beta0_pH[9,3] -0.845 0.555 -2.420 -0.727 -0.126
beta0_pH[10,3] 0.406 0.408 -0.605 0.465 1.035
beta0_pH[11,3] -0.159 0.324 -0.775 -0.165 0.481
beta0_pH[12,3] -0.889 0.358 -1.652 -0.871 -0.253
beta0_pH[13,3] -0.124 0.302 -0.714 -0.127 0.454
beta0_pH[14,3] -0.275 0.258 -0.770 -0.284 0.255
beta0_pH[15,3] -0.718 0.288 -1.312 -0.700 -0.185
beta0_pH[16,3] -0.388 0.285 -0.963 -0.389 0.170
beta1_pH[1,1] 3.043 0.333 2.461 3.021 3.744
beta1_pH[2,1] 2.167 0.311 1.664 2.143 2.841
beta1_pH[3,1] 1.975 0.333 1.424 1.940 2.711
beta1_pH[4,1] 2.387 0.340 1.859 2.345 3.202
beta1_pH[5,1] 2.302 0.347 1.721 2.270 3.095
beta1_pH[6,1] 3.828 1.058 2.368 3.597 6.386
beta1_pH[7,1] 2.708 0.971 0.867 2.637 4.870
beta1_pH[8,1] 4.022 1.027 2.632 3.780 6.583
beta1_pH[9,1] 2.342 0.405 1.716 2.298 3.223
beta1_pH[10,1] 2.407 0.284 1.886 2.395 3.000
beta1_pH[11,1] 3.276 0.211 2.871 3.271 3.702
beta1_pH[12,1] 2.552 0.214 2.143 2.554 2.969
beta1_pH[13,1] 2.981 0.217 2.580 2.971 3.434
beta1_pH[14,1] 3.421 0.217 2.995 3.414 3.870
beta1_pH[15,1] 2.539 0.224 2.133 2.532 2.985
beta1_pH[16,1] 4.157 0.678 3.209 4.030 5.837
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.024 0.165 0.000 0.000 0.023
beta1_pH[4,2] 0.001 0.020 0.000 0.000 0.003
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.702 0.334 6.044 6.698 7.391
beta1_pH[12,2] 6.454 0.452 5.602 6.436 7.389
beta1_pH[13,2] 6.953 0.438 6.102 6.957 7.827
beta1_pH[14,2] 7.259 0.484 6.355 7.237 8.252
beta1_pH[15,2] 6.764 0.371 6.032 6.774 7.492
beta1_pH[16,2] 7.474 0.438 6.648 7.468 8.345
beta1_pH[1,3] 3.801 1.819 1.447 3.436 8.152
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 5.406 25.281 1.726 2.950 7.198
beta1_pH[6,3] 2.628 0.782 1.371 2.598 3.950
beta1_pH[7,3] 2.679 0.437 1.837 2.664 3.555
beta1_pH[8,3] 2.779 0.321 2.148 2.778 3.425
beta1_pH[9,3] 2.927 0.561 2.123 2.834 4.473
beta1_pH[10,3] 2.964 0.473 2.219 2.903 4.125
beta1_pH[11,3] 2.751 0.382 2.007 2.743 3.509
beta1_pH[12,3] 4.149 0.445 3.323 4.140 5.092
beta1_pH[13,3] 1.711 0.327 1.072 1.707 2.366
beta1_pH[14,3] 2.523 0.333 1.855 2.519 3.186
beta1_pH[15,3] 2.011 0.315 1.441 2.000 2.675
beta1_pH[16,3] 1.801 0.317 1.194 1.799 2.437
beta2_pH[1,1] 0.485 0.135 0.290 0.467 0.786
beta2_pH[2,1] 0.565 0.272 0.232 0.510 1.166
beta2_pH[3,1] 0.669 0.510 0.210 0.563 1.832
beta2_pH[4,1] 0.481 0.194 0.212 0.451 0.960
beta2_pH[5,1] 1.392 0.934 0.237 1.265 3.715
beta2_pH[6,1] 0.186 0.069 0.093 0.177 0.337
beta2_pH[7,1] 0.013 0.052 0.000 0.000 0.098
beta2_pH[8,1] 0.243 0.087 0.125 0.226 0.453
beta2_pH[9,1] 0.425 0.195 0.174 0.389 0.895
beta2_pH[10,1] 0.602 0.265 0.289 0.548 1.249
beta2_pH[11,1] 0.774 0.197 0.475 0.744 1.240
beta2_pH[12,1] 1.359 0.491 0.737 1.265 2.494
beta2_pH[13,1] 0.735 0.222 0.405 0.702 1.267
beta2_pH[14,1] 0.831 0.210 0.529 0.797 1.315
beta2_pH[15,1] 0.801 0.283 0.406 0.751 1.500
beta2_pH[16,1] 0.371 0.170 0.165 0.325 0.825
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -0.601 3.880 -8.355 -0.706 7.166
beta2_pH[4,2] -0.595 3.900 -8.400 -0.642 7.296
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.673 4.483 -21.520 -8.638 -3.945
beta2_pH[12,2] -8.122 5.170 -21.160 -7.184 -0.986
beta2_pH[13,2] -7.947 5.232 -21.438 -6.814 -1.660
beta2_pH[14,2] -8.627 4.909 -21.439 -7.507 -2.566
beta2_pH[15,2] -9.348 4.527 -21.361 -8.241 -3.872
beta2_pH[16,2] -9.617 4.543 -21.265 -8.562 -4.010
beta2_pH[1,3] 0.429 1.323 0.057 0.238 1.474
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.648 6.059 0.458 7.528 23.449
beta2_pH[6,3] 8.780 6.146 0.395 7.661 23.552
beta2_pH[7,3] 8.673 6.045 1.029 7.486 23.766
beta2_pH[8,3] 9.589 5.606 1.873 8.528 23.472
beta2_pH[9,3] 8.250 6.373 0.391 7.227 23.455
beta2_pH[10,3] 7.887 6.432 0.443 6.811 23.520
beta2_pH[11,3] -2.166 1.920 -7.314 -1.648 -0.602
beta2_pH[12,3] -2.373 1.841 -7.339 -1.844 -0.927
beta2_pH[13,3] -2.886 2.257 -8.918 -2.200 -0.770
beta2_pH[14,3] -2.789 2.189 -8.879 -2.107 -0.891
beta2_pH[15,3] -2.961 2.188 -8.922 -2.218 -1.036
beta2_pH[16,3] -2.938 2.251 -9.107 -2.228 -0.893
beta3_pH[1,1] 35.918 0.829 34.337 35.886 37.616
beta3_pH[2,1] 33.638 1.240 31.609 33.530 36.384
beta3_pH[3,1] 33.640 1.067 31.637 33.602 35.850
beta3_pH[4,1] 33.828 1.210 31.754 33.734 36.447
beta3_pH[5,1] 27.748 1.150 26.452 27.471 31.082
beta3_pH[6,1] 38.692 3.053 32.969 38.573 44.762
beta3_pH[7,1] 30.666 8.099 18.573 30.049 45.294
beta3_pH[8,1] 39.955 2.150 36.326 39.703 45.019
beta3_pH[9,1] 30.689 1.619 28.045 30.513 34.217
beta3_pH[10,1] 32.714 0.911 31.071 32.666 34.613
beta3_pH[11,1] 30.330 0.477 29.374 30.327 31.258
beta3_pH[12,1] 30.166 0.398 29.363 30.177 30.930
beta3_pH[13,1] 33.144 0.578 32.043 33.129 34.309
beta3_pH[14,1] 32.038 0.462 31.161 32.030 32.963
beta3_pH[15,1] 31.172 0.640 29.931 31.168 32.438
beta3_pH[16,1] 32.040 1.052 30.290 31.915 34.478
beta3_pH[1,2] 30.077 7.889 18.503 29.187 44.854
beta3_pH[2,2] 29.948 7.994 18.582 29.136 45.012
beta3_pH[3,2] 30.208 7.983 18.559 29.127 45.002
beta3_pH[4,2] 29.953 7.932 18.433 29.120 44.927
beta3_pH[5,2] 30.067 8.008 18.460 28.942 44.878
beta3_pH[6,2] 29.853 7.878 18.418 29.078 44.836
beta3_pH[7,2] 29.737 7.966 18.446 28.709 44.942
beta3_pH[8,2] 29.724 7.890 18.437 28.804 44.643
beta3_pH[9,2] 29.902 7.895 18.566 28.816 44.751
beta3_pH[10,2] 30.061 7.935 18.443 29.072 45.002
beta3_pH[11,2] 43.402 0.178 43.119 43.385 43.769
beta3_pH[12,2] 43.188 0.188 42.927 43.141 43.697
beta3_pH[13,2] 43.870 0.145 43.478 43.912 44.041
beta3_pH[14,2] 43.302 0.204 43.049 43.251 43.813
beta3_pH[15,2] 43.412 0.194 43.110 43.395 43.811
beta3_pH[16,2] 43.498 0.190 43.152 43.496 43.847
beta3_pH[1,3] 38.870 3.368 32.660 38.920 45.026
beta3_pH[2,3] 29.997 7.959 18.478 29.070 44.972
beta3_pH[3,3] 30.165 7.968 18.441 29.403 44.890
beta3_pH[4,3] 30.190 7.990 18.467 29.414 45.038
beta3_pH[5,3] 25.654 6.423 18.260 23.795 42.154
beta3_pH[6,3] 27.212 5.040 19.414 25.893 42.941
beta3_pH[7,3] 26.899 0.941 25.403 26.695 29.027
beta3_pH[8,3] 41.494 0.248 41.080 41.495 41.930
beta3_pH[9,3] 33.074 1.321 28.899 33.439 34.140
beta3_pH[10,3] 35.719 0.867 33.301 35.986 36.818
beta3_pH[11,3] 41.803 0.790 40.197 41.833 43.239
beta3_pH[12,3] 41.733 0.379 40.957 41.747 42.480
beta3_pH[13,3] 42.717 0.847 41.144 42.724 44.618
beta3_pH[14,3] 41.092 0.553 39.902 41.114 42.108
beta3_pH[15,3] 42.640 0.647 41.166 42.732 43.668
beta3_pH[16,3] 42.870 0.754 41.140 42.985 44.067
beta0_pelagic[1] 2.218 0.133 1.956 2.219 2.477
beta0_pelagic[2] 1.517 0.126 1.270 1.518 1.770
beta0_pelagic[3] -0.178 0.823 -2.191 -0.024 0.888
beta0_pelagic[4] 0.008 0.848 -1.994 0.151 1.127
beta0_pelagic[5] 1.195 0.248 0.680 1.200 1.675
beta0_pelagic[6] 1.458 0.271 0.868 1.474 1.948
beta0_pelagic[7] 1.693 0.230 1.292 1.670 2.215
beta0_pelagic[8] 1.760 0.204 1.365 1.756 2.197
beta0_pelagic[9] 2.493 0.313 1.876 2.506 3.072
beta0_pelagic[10] 2.528 0.199 2.128 2.537 2.917
beta0_pelagic[11] -0.087 0.536 -1.365 -0.027 0.691
beta0_pelagic[12] 1.675 0.145 1.393 1.679 1.949
beta0_pelagic[13] 0.296 0.216 -0.190 0.316 0.665
beta0_pelagic[14] -0.114 0.291 -0.774 -0.090 0.386
beta0_pelagic[15] -0.267 0.141 -0.555 -0.266 0.003
beta0_pelagic[16] 0.243 0.326 -0.538 0.327 0.677
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.592 1.399 0.000 1.325 5.569
beta1_pelagic[4] 1.324 1.087 0.000 1.140 3.868
beta1_pelagic[5] -0.080 0.312 -0.687 -0.077 0.526
beta1_pelagic[6] -0.088 0.449 -0.862 -0.136 0.754
beta1_pelagic[7] -0.010 0.350 -0.677 -0.007 0.672
beta1_pelagic[8] -0.002 0.277 -0.532 -0.008 0.572
beta1_pelagic[9] 0.192 0.492 -0.790 0.300 0.959
beta1_pelagic[10] 0.065 0.259 -0.464 0.065 0.577
beta1_pelagic[11] 4.011 1.289 2.210 3.857 7.053
beta1_pelagic[12] 2.809 0.338 2.226 2.801 3.480
beta1_pelagic[13] 2.962 0.766 1.762 2.849 4.785
beta1_pelagic[14] 4.435 1.076 2.871 4.246 6.841
beta1_pelagic[15] 2.927 0.272 2.382 2.930 3.431
beta1_pelagic[16] 3.813 1.121 2.681 3.357 6.782
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.652 2.888 0.000 0.116 5.959
beta2_pelagic[4] 1.380 4.457 0.000 0.218 11.121
beta2_pelagic[5] -0.004 0.666 -1.366 -0.003 1.382
beta2_pelagic[6] -0.108 0.689 -1.500 -0.150 1.279
beta2_pelagic[7] -0.010 0.687 -1.414 0.000 1.358
beta2_pelagic[8] -0.003 0.627 -1.359 0.001 1.292
beta2_pelagic[9] 0.181 0.688 -1.281 0.235 1.495
beta2_pelagic[10] 0.048 0.627 -1.268 0.033 1.392
beta2_pelagic[11] 1.360 3.294 0.095 0.223 11.703
beta2_pelagic[12] 5.735 4.895 1.008 4.243 19.694
beta2_pelagic[13] 0.790 1.454 0.183 0.450 3.464
beta2_pelagic[14] 0.327 0.290 0.155 0.282 0.729
beta2_pelagic[15] 5.921 4.905 1.170 4.489 19.672
beta2_pelagic[16] 4.188 5.279 0.178 2.359 18.381
beta3_pelagic[1] 29.988 7.959 18.535 28.932 44.894
beta3_pelagic[2] 30.030 7.795 18.514 29.191 44.787
beta3_pelagic[3] 29.924 6.606 18.847 29.336 44.245
beta3_pelagic[4] 26.447 6.115 18.603 25.160 42.670
beta3_pelagic[5] 30.500 8.165 18.542 29.290 45.230
beta3_pelagic[6] 31.585 6.838 18.876 31.604 44.242
beta3_pelagic[7] 29.285 7.275 18.522 28.430 44.960
beta3_pelagic[8] 29.746 8.092 18.377 28.531 44.942
beta3_pelagic[9] 30.838 6.200 18.935 30.983 43.073
beta3_pelagic[10] 29.410 8.151 18.350 27.891 44.889
beta3_pelagic[11] 42.226 2.209 36.743 42.836 45.599
beta3_pelagic[12] 43.473 0.300 42.984 43.460 44.043
beta3_pelagic[13] 42.820 1.333 40.334 42.769 45.595
beta3_pelagic[14] 42.480 1.652 39.104 42.467 45.603
beta3_pelagic[15] 43.158 0.282 42.442 43.172 43.663
beta3_pelagic[16] 43.179 0.894 41.123 43.223 45.286
mu_beta0_pelagic[1] 0.827 1.049 -1.570 0.933 2.763
mu_beta0_pelagic[2] 1.827 0.371 1.058 1.834 2.566
mu_beta0_pelagic[3] 0.270 0.483 -0.758 0.291 1.232
tau_beta0_pelagic[1] 0.736 1.017 0.049 0.400 3.548
tau_beta0_pelagic[2] 2.716 2.632 0.291 2.006 8.956
tau_beta0_pelagic[3] 1.487 1.168 0.155 1.180 4.561
beta0_yellow[1] -0.504 0.180 -0.861 -0.497 -0.186
beta0_yellow[2] 0.521 0.164 0.198 0.524 0.826
beta0_yellow[3] -0.272 0.197 -0.657 -0.270 0.095
beta0_yellow[4] 0.985 0.307 0.205 1.009 1.436
beta0_yellow[5] -0.324 0.349 -0.988 -0.331 0.372
beta0_yellow[6] 1.134 0.169 0.805 1.134 1.458
beta0_yellow[7] 1.070 0.157 0.768 1.067 1.390
beta0_yellow[8] 1.015 0.158 0.715 1.008 1.328
beta0_yellow[9] 0.671 0.161 0.354 0.675 0.976
beta0_yellow[10] 0.582 0.143 0.297 0.583 0.854
beta0_yellow[11] -1.927 0.439 -2.807 -1.917 -1.065
beta0_yellow[12] -3.686 0.434 -4.634 -3.662 -2.926
beta0_yellow[13] -3.714 0.494 -4.773 -3.679 -2.844
beta0_yellow[14] -2.099 0.536 -3.036 -2.129 -0.845
beta0_yellow[15] -2.810 0.412 -3.697 -2.785 -2.069
beta0_yellow[16] -2.367 0.449 -3.213 -2.373 -1.436
beta1_yellow[1] 0.720 3.424 0.000 0.199 2.489
beta1_yellow[2] 1.026 0.341 0.536 1.000 1.612
beta1_yellow[3] 0.595 0.290 0.000 0.606 1.124
beta1_yellow[4] 0.889 0.870 0.000 0.933 3.248
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 2.067 0.436 1.190 2.068 2.917
beta1_yellow[12] 2.467 0.453 1.661 2.425 3.436
beta1_yellow[13] 2.816 0.488 1.965 2.777 3.831
beta1_yellow[14] 2.178 0.521 0.966 2.196 3.131
beta1_yellow[15] 2.051 0.411 1.275 2.038 2.889
beta1_yellow[16] 2.114 0.446 1.201 2.126 2.998
beta2_yellow[1] -4.965 3.456 -12.527 -4.467 -0.120
beta2_yellow[2] -4.891 3.397 -12.182 -4.371 -0.279
beta2_yellow[3] -4.804 3.426 -12.223 -4.350 -0.244
beta2_yellow[4] -4.591 3.622 -12.544 -3.986 -0.091
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -6.133 3.383 -13.940 -5.632 -1.332
beta2_yellow[12] -6.402 3.149 -13.535 -6.001 -1.790
beta2_yellow[13] -6.222 3.011 -12.889 -5.879 -1.840
beta2_yellow[14] -8.204 5.602 -21.872 -6.824 -1.139
beta2_yellow[15] -5.834 3.374 -13.863 -5.305 -1.180
beta2_yellow[16] -6.531 3.380 -14.485 -6.095 -1.687
beta3_yellow[1] 27.613 7.684 18.403 24.907 44.521
beta3_yellow[2] 29.143 1.726 26.860 28.832 32.921
beta3_yellow[3] 32.858 3.745 22.423 32.905 41.516
beta3_yellow[4] 29.558 5.338 19.795 28.057 43.114
beta3_yellow[5] 30.214 7.957 18.553 29.269 44.990
beta3_yellow[6] 30.151 7.952 18.484 29.194 44.878
beta3_yellow[7] 30.225 8.044 18.471 29.130 45.067
beta3_yellow[8] 30.177 7.911 18.389 29.474 44.823
beta3_yellow[9] 29.977 7.850 18.484 29.089 44.857
beta3_yellow[10] 30.106 7.907 18.449 29.177 44.861
beta3_yellow[11] 45.298 0.530 44.032 45.381 45.977
beta3_yellow[12] 43.312 0.368 42.521 43.282 44.015
beta3_yellow[13] 44.902 0.409 44.010 44.983 45.616
beta3_yellow[14] 44.067 1.513 41.889 44.213 45.808
beta3_yellow[15] 45.109 0.542 44.127 45.060 45.968
beta3_yellow[16] 44.486 0.663 43.313 44.463 45.797
mu_beta0_yellow[1] 0.160 0.563 -1.051 0.163 1.294
mu_beta0_yellow[2] 0.655 0.354 -0.106 0.667 1.303
mu_beta0_yellow[3] -2.410 0.667 -3.449 -2.508 -0.686
tau_beta0_yellow[1] 1.640 1.962 0.081 1.083 6.430
tau_beta0_yellow[2] 3.139 3.707 0.244 2.157 11.754
tau_beta0_yellow[3] 1.433 2.075 0.093 0.896 5.692
beta0_black[1] -0.073 0.162 -0.389 -0.070 0.238
beta0_black[2] 1.916 0.128 1.660 1.915 2.171
beta0_black[3] 1.324 0.137 1.066 1.321 1.591
beta0_black[4] 2.433 0.136 2.159 2.436 2.703
beta0_black[5] 1.614 1.939 -3.002 1.668 5.555
beta0_black[6] 1.591 1.893 -3.095 1.709 5.349
beta0_black[7] 1.513 2.021 -3.218 1.617 5.429
beta0_black[8] 1.303 0.232 0.846 1.304 1.762
beta0_black[9] 2.454 0.251 1.971 2.449 2.951
beta0_black[10] 1.475 0.131 1.223 1.473 1.736
beta0_black[11] 3.482 0.154 3.182 3.482 3.785
beta0_black[12] 4.870 0.177 4.516 4.870 5.207
beta0_black[13] -0.150 0.323 -0.735 -0.130 0.338
beta0_black[14] 2.853 0.161 2.540 2.853 3.166
beta0_black[15] 1.296 0.159 0.994 1.294 1.614
beta0_black[16] 4.272 0.164 3.964 4.273 4.587
beta2_black[1] 109.248 427.008 0.552 4.922 1785.167
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.158 2.484 -11.403 -1.314 -0.223
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.788 1.179 39.786 41.990 43.299
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.041 1.516 36.462 39.262 40.656
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.264 0.196 -0.648 -0.263 0.117
beta4_black[2] 0.240 0.189 -0.130 0.238 0.608
beta4_black[3] -0.941 0.197 -1.326 -0.944 -0.549
beta4_black[4] 0.422 0.220 -0.003 0.420 0.868
beta4_black[5] 0.250 2.451 -4.595 0.180 5.072
beta4_black[6] 0.162 2.349 -4.644 0.146 4.791
beta4_black[7] 0.192 2.559 -4.585 0.117 5.066
beta4_black[8] -0.710 0.374 -1.459 -0.711 0.007
beta4_black[9] 1.457 1.030 -0.134 1.322 3.766
beta4_black[10] 0.027 0.189 -0.332 0.024 0.401
beta4_black[11] -0.697 0.216 -1.103 -0.701 -0.280
beta4_black[12] 0.178 0.321 -0.414 0.163 0.834
beta4_black[13] -1.180 0.229 -1.626 -1.178 -0.728
beta4_black[14] -0.182 0.237 -0.636 -0.188 0.296
beta4_black[15] -0.890 0.222 -1.346 -0.884 -0.472
beta4_black[16] -0.590 0.231 -1.038 -0.591 -0.138
mu_beta0_black[1] 1.303 0.909 -0.743 1.327 3.067
mu_beta0_black[2] 1.587 0.907 -0.547 1.661 3.274
mu_beta0_black[3] 2.501 1.002 0.334 2.555 4.371
tau_beta0_black[1] 0.645 0.610 0.057 0.444 2.275
tau_beta0_black[2] 2.056 3.787 0.059 0.838 11.120
tau_beta0_black[3] 0.231 0.155 0.049 0.192 0.624
beta0_dsr[11] -2.890 0.290 -3.466 -2.878 -2.323
beta0_dsr[12] 4.548 0.283 4.008 4.550 5.105
beta0_dsr[13] -1.370 0.346 -2.023 -1.354 -0.786
beta0_dsr[14] -3.660 0.501 -4.626 -3.659 -2.672
beta0_dsr[15] -1.945 0.283 -2.489 -1.947 -1.371
beta0_dsr[16] -2.988 0.365 -3.733 -2.987 -2.260
beta1_dsr[11] 4.827 0.301 4.254 4.823 5.419
beta1_dsr[12] 7.150 18.397 2.193 5.053 22.727
beta1_dsr[13] 2.883 0.392 2.278 2.860 3.566
beta1_dsr[14] 6.326 0.529 5.276 6.337 7.356
beta1_dsr[15] 3.349 0.291 2.784 3.346 3.917
beta1_dsr[16] 5.805 0.381 5.052 5.794 6.595
beta2_dsr[11] -8.219 2.359 -13.692 -7.894 -4.574
beta2_dsr[12] -7.026 2.617 -12.934 -6.822 -2.413
beta2_dsr[13] -6.401 2.709 -12.098 -6.336 -1.322
beta2_dsr[14] -6.175 2.677 -11.896 -6.123 -1.778
beta2_dsr[15] -7.690 2.412 -13.417 -7.398 -3.803
beta2_dsr[16] -7.912 2.362 -13.528 -7.600 -4.219
beta3_dsr[11] 43.488 0.149 43.217 43.485 43.784
beta3_dsr[12] 33.980 0.754 32.204 34.119 34.814
beta3_dsr[13] 43.262 0.352 42.797 43.202 43.891
beta3_dsr[14] 43.354 0.248 43.077 43.277 43.993
beta3_dsr[15] 43.504 0.187 43.155 43.505 43.848
beta3_dsr[16] 43.434 0.158 43.167 43.418 43.754
beta4_dsr[11] 0.587 0.221 0.165 0.585 1.030
beta4_dsr[12] 0.247 0.452 -0.655 0.237 1.180
beta4_dsr[13] -0.155 0.222 -0.604 -0.148 0.256
beta4_dsr[14] 0.144 0.258 -0.373 0.153 0.634
beta4_dsr[15] 0.718 0.218 0.307 0.712 1.155
beta4_dsr[16] 0.152 0.241 -0.328 0.148 0.638
beta0_slope[11] -1.850 0.150 -2.139 -1.849 -1.550
beta0_slope[12] -4.474 0.258 -4.993 -4.468 -4.004
beta0_slope[13] -1.333 0.182 -1.728 -1.318 -1.012
beta0_slope[14] -2.680 0.169 -3.009 -2.682 -2.352
beta0_slope[15] -1.334 0.148 -1.631 -1.331 -1.051
beta0_slope[16] -2.732 0.161 -3.051 -2.729 -2.416
beta1_slope[11] 4.485 0.224 4.055 4.484 4.933
beta1_slope[12] 3.982 0.434 3.142 3.987 4.841
beta1_slope[13] 2.709 0.420 2.204 2.641 3.875
beta1_slope[14] 6.326 0.425 5.515 6.317 7.209
beta1_slope[15] 2.995 0.209 2.565 3.000 3.390
beta1_slope[16] 5.287 0.292 4.695 5.282 5.868
beta2_slope[11] 8.587 2.315 5.070 8.242 14.062
beta2_slope[12] 6.704 2.948 1.235 6.665 12.976
beta2_slope[13] 5.325 2.946 0.428 5.260 11.291
beta2_slope[14] 6.389 2.528 2.216 6.282 11.828
beta2_slope[15] 8.298 2.478 4.463 7.977 14.127
beta2_slope[16] 7.712 2.222 4.199 7.443 12.924
beta3_slope[11] 43.464 0.134 43.224 43.459 43.733
beta3_slope[12] 43.355 0.286 42.847 43.316 43.961
beta3_slope[13] 43.459 0.375 42.908 43.410 44.042
beta3_slope[14] 43.268 0.137 43.093 43.239 43.607
beta3_slope[15] 43.484 0.165 43.190 43.481 43.799
beta3_slope[16] 43.372 0.142 43.159 43.354 43.697
beta4_slope[11] -0.731 0.166 -1.053 -0.730 -0.410
beta4_slope[12] -1.142 0.458 -2.082 -1.106 -0.323
beta4_slope[13] 0.082 0.166 -0.246 0.083 0.417
beta4_slope[14] -0.090 0.197 -0.465 -0.095 0.305
beta4_slope[15] -0.770 0.160 -1.088 -0.771 -0.459
beta4_slope[16] -0.162 0.177 -0.514 -0.161 0.187
sigma_H[1] 0.204 0.055 0.108 0.200 0.325
sigma_H[2] 0.171 0.030 0.119 0.169 0.235
sigma_H[3] 0.196 0.042 0.122 0.194 0.285
sigma_H[4] 0.422 0.077 0.297 0.413 0.591
sigma_H[5] 0.991 0.205 0.626 0.973 1.416
sigma_H[6] 0.399 0.199 0.039 0.395 0.821
sigma_H[7] 0.314 0.066 0.212 0.305 0.469
sigma_H[8] 0.418 0.088 0.278 0.409 0.613
sigma_H[9] 0.527 0.128 0.332 0.510 0.828
sigma_H[10] 0.215 0.042 0.139 0.212 0.302
sigma_H[11] 0.278 0.046 0.199 0.275 0.378
sigma_H[12] 0.430 0.164 0.205 0.399 0.776
sigma_H[13] 0.214 0.037 0.151 0.210 0.293
sigma_H[14] 0.509 0.090 0.351 0.502 0.703
sigma_H[15] 0.246 0.040 0.178 0.243 0.335
sigma_H[16] 0.223 0.044 0.150 0.219 0.317
lambda_H[1] 3.103 3.809 0.180 1.846 13.354
lambda_H[2] 8.364 7.702 0.794 6.265 29.090
lambda_H[3] 6.432 9.575 0.296 3.133 33.472
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.899 9.269 0.037 1.051 26.881
lambda_H[6] 7.027 12.933 0.008 0.800 46.507
lambda_H[7] 0.011 0.008 0.002 0.009 0.032
lambda_H[8] 8.432 10.776 0.107 4.672 37.806
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.306 0.529 0.032 0.200 1.142
lambda_H[11] 0.278 0.451 0.010 0.130 1.399
lambda_H[12] 4.728 6.009 0.182 2.706 21.154
lambda_H[13] 3.569 3.263 0.228 2.670 12.293
lambda_H[14] 3.308 4.216 0.227 1.930 14.373
lambda_H[15] 0.025 0.037 0.003 0.016 0.097
lambda_H[16] 0.822 1.324 0.041 0.422 3.914
mu_lambda_H[1] 4.366 1.896 1.319 4.098 8.495
mu_lambda_H[2] 3.748 1.912 0.602 3.579 7.849
mu_lambda_H[3] 3.490 1.823 0.785 3.240 7.624
sigma_lambda_H[1] 8.728 4.327 2.223 8.002 18.642
sigma_lambda_H[2] 8.238 4.574 1.031 7.685 18.048
sigma_lambda_H[3] 6.303 3.989 0.987 5.510 16.209
beta_H[1,1] 6.931 1.040 4.411 7.083 8.521
beta_H[2,1] 9.880 0.506 8.826 9.902 10.810
beta_H[3,1] 7.997 0.767 6.160 8.094 9.269
beta_H[4,1] 9.208 7.936 -7.511 9.514 23.804
beta_H[5,1] 0.138 2.263 -4.619 0.337 4.037
beta_H[6,1] 3.108 3.987 -6.674 4.478 7.713
beta_H[7,1] -0.679 6.161 -13.644 -0.370 10.258
beta_H[8,1] 1.349 3.578 -2.196 1.255 3.535
beta_H[9,1] 12.948 5.601 1.853 12.869 23.933
beta_H[10,1] 7.092 1.680 3.639 7.119 10.282
beta_H[11,1] 5.180 3.580 -2.831 5.993 10.056
beta_H[12,1] 2.635 1.070 0.761 2.553 4.956
beta_H[13,1] 9.020 1.020 7.060 9.127 10.514
beta_H[14,1] 2.208 1.057 0.053 2.210 4.381
beta_H[15,1] -6.173 3.796 -12.906 -6.426 1.911
beta_H[16,1] 3.517 2.692 -0.713 3.212 9.881
beta_H[1,2] 7.903 0.241 7.416 7.907 8.361
beta_H[2,2] 10.029 0.137 9.758 10.029 10.302
beta_H[3,2] 8.953 0.196 8.563 8.950 9.337
beta_H[4,2] 3.615 1.505 0.766 3.552 6.754
beta_H[5,2] 1.926 0.931 0.074 1.940 3.686
beta_H[6,2] 5.741 1.049 3.247 5.914 7.343
beta_H[7,2] 2.995 1.181 0.904 2.900 5.413
beta_H[8,2] 3.007 1.023 1.350 3.142 4.208
beta_H[9,2] 3.522 1.120 1.494 3.489 5.865
beta_H[10,2] 8.204 0.343 7.486 8.218 8.855
beta_H[11,2] 9.758 0.648 8.837 9.631 11.228
beta_H[12,2] 3.938 0.375 3.244 3.924 4.672
beta_H[13,2] 9.120 0.266 8.668 9.103 9.646
beta_H[14,2] 4.033 0.351 3.362 4.026 4.742
beta_H[15,2] 11.367 0.684 9.942 11.403 12.635
beta_H[16,2] 4.533 0.802 3.021 4.513 6.145
beta_H[1,3] 8.443 0.238 8.012 8.430 8.958
beta_H[2,3] 10.064 0.116 9.834 10.065 10.301
beta_H[3,3] 9.614 0.164 9.298 9.611 9.951
beta_H[4,3] -2.575 0.897 -4.345 -2.554 -0.837
beta_H[5,3] 3.802 0.606 2.499 3.821 4.953
beta_H[6,3] 8.003 1.187 6.384 7.625 10.577
beta_H[7,3] -3.118 0.686 -4.453 -3.104 -1.772
beta_H[8,3] 5.243 0.476 4.642 5.178 6.209
beta_H[9,3] -2.863 0.746 -4.366 -2.860 -1.382
beta_H[10,3] 8.683 0.277 8.160 8.679 9.232
beta_H[11,3] 8.539 0.290 7.927 8.563 9.048
beta_H[12,3] 5.246 0.323 4.508 5.279 5.764
beta_H[13,3] 8.843 0.175 8.475 8.848 9.176
beta_H[14,3] 5.719 0.279 5.120 5.738 6.213
beta_H[15,3] 10.362 0.320 9.716 10.358 10.995
beta_H[16,3] 6.223 0.612 4.846 6.292 7.238
beta_H[1,4] 8.256 0.176 7.884 8.269 8.570
beta_H[2,4] 10.131 0.122 9.873 10.138 10.350
beta_H[3,4] 10.119 0.161 9.777 10.132 10.399
beta_H[4,4] 11.812 0.460 10.921 11.817 12.700
beta_H[5,4] 5.457 0.723 4.245 5.370 7.092
beta_H[6,4] 7.053 0.919 4.968 7.316 8.309
beta_H[7,4] 8.325 0.358 7.604 8.326 9.024
beta_H[8,4] 6.706 0.247 6.218 6.720 7.130
beta_H[9,4] 7.213 0.474 6.287 7.197 8.186
beta_H[10,4] 7.749 0.237 7.300 7.742 8.220
beta_H[11,4] 9.391 0.197 9.010 9.391 9.787
beta_H[12,4] 7.136 0.211 6.726 7.139 7.561
beta_H[13,4] 9.046 0.140 8.760 9.050 9.322
beta_H[14,4] 7.737 0.221 7.290 7.736 8.180
beta_H[15,4] 9.470 0.238 9.005 9.468 9.933
beta_H[16,4] 9.352 0.238 8.929 9.334 9.859
beta_H[1,5] 8.984 0.146 8.696 8.985 9.269
beta_H[2,5] 10.783 0.094 10.608 10.784 10.976
beta_H[3,5] 10.919 0.169 10.616 10.912 11.275
beta_H[4,5] 8.374 0.472 7.480 8.363 9.363
beta_H[5,5] 5.424 0.578 4.065 5.468 6.447
beta_H[6,5] 8.807 0.635 7.893 8.664 10.310
beta_H[7,5] 6.747 0.346 6.091 6.743 7.458
beta_H[8,5] 8.212 0.211 7.840 8.198 8.648
beta_H[9,5] 8.206 0.485 7.255 8.209 9.170
beta_H[10,5] 10.089 0.233 9.630 10.089 10.547
beta_H[11,5] 11.502 0.230 11.051 11.511 11.958
beta_H[12,5] 8.488 0.194 8.095 8.486 8.881
beta_H[13,5] 10.009 0.130 9.758 10.009 10.269
beta_H[14,5] 9.207 0.230 8.783 9.201 9.693
beta_H[15,5] 11.159 0.242 10.687 11.154 11.637
beta_H[16,5] 9.923 0.180 9.561 9.926 10.267
beta_H[1,6] 10.179 0.187 9.847 10.168 10.587
beta_H[2,6] 11.515 0.106 11.304 11.516 11.728
beta_H[3,6] 10.817 0.160 10.477 10.828 11.103
beta_H[4,6] 12.892 0.821 11.242 12.898 14.454
beta_H[5,6] 5.883 0.605 4.748 5.866 7.125
beta_H[6,6] 8.760 0.683 6.933 8.875 9.751
beta_H[7,6] 9.893 0.594 8.705 9.908 11.042
beta_H[8,6] 9.512 0.271 8.982 9.530 9.951
beta_H[9,6] 8.464 0.803 6.919 8.462 10.100
beta_H[10,6] 9.502 0.324 8.793 9.530 10.072
beta_H[11,6] 10.816 0.353 10.078 10.838 11.441
beta_H[12,6] 9.376 0.258 8.878 9.364 9.914
beta_H[13,6] 11.043 0.167 10.758 11.032 11.400
beta_H[14,6] 9.819 0.287 9.245 9.826 10.363
beta_H[15,6] 10.850 0.419 10.018 10.864 11.667
beta_H[16,6] 10.526 0.246 9.989 10.539 10.988
beta_H[1,7] 10.931 0.827 9.012 11.033 12.279
beta_H[2,7] 12.204 0.436 11.319 12.216 13.013
beta_H[3,7] 10.556 0.652 9.137 10.620 11.636
beta_H[4,7] 2.433 4.170 -5.580 2.366 10.978
beta_H[5,7] 6.373 1.726 3.061 6.323 10.148
beta_H[6,7] 9.638 2.475 4.763 9.544 15.734
beta_H[7,7] 10.418 2.986 4.640 10.340 16.515
beta_H[8,7] 10.942 1.007 9.302 10.903 12.668
beta_H[9,7] 4.479 4.089 -3.676 4.474 12.759
beta_H[10,7] 9.848 1.455 7.276 9.728 13.059
beta_H[11,7] 10.990 1.724 7.749 10.874 14.731
beta_H[12,7] 9.987 0.939 7.862 10.062 11.546
beta_H[13,7] 11.675 0.765 9.806 11.779 12.831
beta_H[14,7] 10.374 0.961 8.429 10.434 12.072
beta_H[15,7] 11.948 2.205 7.617 11.900 16.284
beta_H[16,7] 12.381 1.310 10.240 12.202 15.350
beta0_H[1] 9.185 12.615 -16.644 9.237 34.407
beta0_H[2] 10.766 6.229 -1.781 10.720 24.098
beta0_H[3] 9.958 9.482 -9.610 9.877 29.883
beta0_H[4] 9.275 186.243 -377.831 10.793 375.663
beta0_H[5] 3.867 22.594 -46.983 4.354 48.464
beta0_H[6] 6.553 52.766 -105.633 7.517 114.488
beta0_H[7] 0.729 149.129 -308.489 0.917 298.497
beta0_H[8] 7.236 28.819 -17.510 6.513 29.382
beta0_H[9] -0.568 121.965 -255.230 1.304 232.504
beta0_H[10] 8.400 32.112 -61.261 8.510 73.411
beta0_H[11] 9.178 52.727 -95.862 8.884 122.996
beta0_H[12] 6.920 13.296 -15.010 6.634 29.644
beta0_H[13] 9.962 11.852 -12.294 9.840 30.711
beta0_H[14] 7.134 11.450 -15.797 7.092 29.070
beta0_H[15] 7.265 108.308 -216.160 6.372 227.089
beta0_H[16] 7.730 25.988 -45.085 7.597 62.890